How one short question can help you escape the fixed-pie trap and problem-solve creatively.
A man died, leaving 17 camels to his three children. The eldest was to receive half the camels, the middle child one-third, and the youngest one-ninth.
They couldn’t figure out how to divide 17 camels in accordance with their father’s last wishes. After arguing for several days, they consulted a wise old woman for help.
She offered to lend them her one camel. With 18 camels, the first child took 9, the second took 6, and the third took 2.
One camel remained, and they returned it to the woman.
This delightful story from Jay Rothman, author of the classic, Resolving Identity-Based Conflict in Nations, Organizations, and Communities, shows how fixed-pie thinking traps us in disagreement.
“Fixed-pie thinking” is the zero-sum mindset that one person’s gain must be the other person’s loss. Mediators use the phrase “expand the pie” to convey the idea that good problem-solving pushes us to think past the fixed-pie fallacy.
And there’s one question in particular that I’ve found helps expand the pie.
One reason we get stuck
When Nobel laureate Daniel Kahneman studied decision-making, he found that we feel loss roughly twice as intensely as we feel gain. This “loss aversion” means that when we’re negotiating the division of resources, preventing loss tends to overshadow pursuing gain.
Zero-sum problems — or problems that masquerade as zero-sum — feed loss aversion.
The power of adding
Adding resources breaks the fixed-pie trap by shifting our attention from defense to possibility. When we’re stuck in division mode, we focus on protecting our share. But when someone adds a resource, even a small one, the frame changes. We’re no longer just defending; we’re looking at what becomes newly possible.
The wise woman’s single camel didn’t change the fundamental inheritance; it changed what was mathematically possible. That’s what the right resource does: It makes new solutions visible.
To add the right resource, we need to identify what perceived shortage is feeding zero-sum thinking. The question that cuts through the noise is:
What don’t we have enough of?
Sometimes the answer is money. Often it’s not. It might be time, information, help, authority, or something else entirely — like a camel.
What we can add
Here are resources that most often unlock stuck disagreements and ways to add them:
- Time: Ways to add time include moving deadlines or start dates, splitting a project into phases, staggering competing schedules, and running things in parallel instead of sequentially.
- Money. Ways to add money include trading skills or services instead of paying cash, borrowing or renting instead of buying, doing parts ourselves and paying only for skilled work, and spreading the work out into phases.
- Help: Ways to add help include spreading the task across multiple team members, trading a favor, and posting in a local social media group.
- Information: Ways to add information include confirming whether perceived constraints (deadline, budget, requirements) are real, conducting a tiny experiment to test assumptions, and researching what others have done.
- Physical things: We add to physical resources by renting, borrowing, buying, and sharing.
- Permission or authority: Ways to increase authority for moving forward include requesting explicit approval, requesting a one-time exception, and clarifying the rules or perceived limits.
A case study
Two project managers were locked in a battle over Anna, a senior engineer. Both needed her for critical projects launching in the same quarter. They’d tried the obvious solutions: splitting her time 50/50 (neither project would hit deadlines), prioritizing one project over the other (the deprioritized PM would appeal to upper management), and hiring another engineer (would take months to onboard). Every solution was a loss for someone.
When their director asked, “What don’t we have enough of?” the first answer was “Anna’s time.” But pushing further — “What specifically about Anna are you short on?”— revealed something different.
One PM needed Anna because she was the only person who understood how the legacy payment system worked. The other needed her because she was the only one trusted to make architectural decisions without endless review cycles.
The actual shortage wasn’t Anna, per se. It was a shortage of documentation for the legacy payment system and decision-making authority.
Once the actual shortages were clear, they added information (Anna spent three days writing comprehensive documentation of the payment system), help (they trained two other engineers using the documentation), and authority (one of the PMs requested and received authority to make architectural calls within defined parameters, removing the bottleneck of waiting for Anna’s judgment).
Anna ended up spending minimal time on either project. The conflict was resolved not by dividing Anna’s time, but by adding the resources they were actually short on.
Over to you
The next time you’re in a disagreement that feels stuck, pause and ask, “What don’t we have enough of?” Be specific. “Not enough money” is too broad. “Not enough cash to cover both options before the deadline” is better.
Once you’ve identified the actual shortage, ask, “How could we get more of that, even a little?” You only need to add enough of the resource to stop the situation from being zero-sum. Sometimes all you need is a borrowed camel.
The wise woman didn’t solve the inheritance problem by being clever about division. She solved it by making it not a division problem at all.